Bryan Dimler

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math.DG2025

Uniqueness in the Plateau problem for calibrated currents

Bryan Dimler, Chen-Kuan Lee

We show that every compactly supported smoothly calibrated integral current with connected $C^{3, α}$ boundary is the unique solution to the oriented Plateau problem for its boundar…

math.DG2024

Minimal submanifolds with multiple isolated singularities

Bryan Dimler

We extend Smale's singular bridge principle [Ann. of Math. 130 (1989), 603-642] for $n$ -dimensional strictly stable minimal cones in $R^{n + 1}$ $(n \geq 7$ ) to arbitrary co…

math.DG2024

Strict stability of calibrated cones

Bryan Dimler, Jooho Lee

We study the strict stability of calibrated cones with an isolated singularity. For special Lagrangian cones and coassociative cones, we prove the strict stability. In the complex…